{"paper":{"title":"Mutual compatibility/incompatibility of quasi-Hermitian quantum observables","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Miloslav Znojil","submitted_at":"2025-05-01T18:41:27Z","abstract_excerpt":"In the framework of quasi-Hermitian quantum mechanics the eligible operators of observables may be non-Hermitian, $A_j\\neq A_j^\\dagger$, $j=1,2, \\ldots,K$. In principle, the standard probabilistic interpretation of the theory can be re-established via a reconstruction of physical inner-product metric $\\Theta\\neq I$ guaranteeing the quasi-Hermiticity $A_j^\\dagger \\,\\Theta=\\Theta\\,A_j$. The task is easy at $K=1$ because there are many eligible metrics $\\Theta=\\Theta(A_1)$. In our paper the next case with $K=2$ is analyzed. The criteria of the existence of a shared metric $\\Theta=\\Theta(A_1,A_2)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.00791","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.00791/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}